Algebraic Representation of Correlation Functions in Integrable Spin Chains

2006/01/22 by H. Boos, M. Jimbo, T. Miwa +3 · 7 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebra over a field #Algebraic number #Algebraic structures and combinatorial models #Chain (unit) #Combinatorics #Generalization #Homogeneous #Integrable system #Invariant (physics) #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Waves and Solitons #Physics #Pure mathematics #Quantum #Quantum mechanics #Representation (politics) #Spin (aerodynamics) #hep-th #math-ph #math.MP #math.QA

paper · pdf · doi:10.1007/s00023-006-0285-5

published as AnnalesHenriPoincare7:1395-1428,2006 · 31 pages, no figure

arxiv created 2006/01/22 · openalex publication_date 2006/11/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Taking the XXZ chain as the main example, we give a review of an algebraic representation of correlation functions in integrable spin chains obtained recently. We rewrite the previous formulas in a form which works equally well for the physically interesting homogeneous chains. We discuss also the case of quantum group invariant operators and generalization to the XYZ chain.

Citations

• On the algebraic Bethe Ansatz approach to the correlation functions of the XXZ spin-1/2 Heisenberg chain
• Third-neighbour and other four-point correlation functions of spin-1/2XXZchain
• Next-nearest-neighbour correlation functions of the spin-1/2XXZchain at the critical region

Cited by

• Universal R-matrix and functional relations
• Factorization of the finite temperature correlation functions of theXXZchain in a magnetic field
• Density matrices for finite segments of Heisenberg chains of arbitrary length
• Adjacent spin operator dynamical structure factor of theS= 1/2 Heisenberg chain
• Worldsheet form factors in AdS/CFT
• Stationary behaviour of observables after a quantum quench in the spin-1/2 Heisenberg XXZ chain
• Emptiness formation probability in the domain-wall six-vertex model